Falloff of the Weyl scalars in binary black hole spacetimes

TL;DR

This paper confirms the peeling theorem's predictions for Weyl scalar falloff in binary black hole mergers through numerical simulations, showing all scalars decay as expected at large distances.

Contribution

The study provides the first numerical verification that all Weyl scalars in binary black hole spacetimes follow the peeling theorem's falloff rates.

Findings

All Weyl scalars decay according to the peeling theorem.

Numerical simulations align with theoretical predictions.

Supports the interpretation of Psi_4 as outgoing gravitational radiation.

Abstract

The peeling theorem of general relativity predicts that the Weyl curvature scalars Psi_n (n=0...4), when constructed from a suitable null tetrad in an asymptotically flat spacetime, fall off asymptotically as r^(n-5) along outgoing radial null geodesics. This leads to the interpretation of Psi_4 as outgoing gravitational radiation at large distances from the source. We have performed numerical simulations in full general relativity of a binary black hole inspiral and merger, and have computed the Weyl scalars in the standard tetrad used in numerical relativity. In contrast with previous results, we observe that all the Weyl scalars fall off according to the predictions of the theorem.